Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #1817 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator | C22×C61 | C22×C8 |
| Fitting | C23×C4×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| hypercenter | C23×C4 | #6923 |
| hypocenter | C61 | #1817 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
380 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=f,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^11,h^c=h^60,h^f=h^60536 conjugacy classes — view the full character table.
| maximal subgroup of | #30593967, #30593975, #30593980, … |
| maximal normal subgroup of | #30593967, #30593975, #30593980, … |
| maximal quotient of | #30599208, #30599211, #30599215, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20401);